Nonlocal boundary value problems for a fractional-order convection-diffusion equation

M. Kh. Beshtokov   ; V. A. Vogahova

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 29 (2019) no. 4, pp. 459-482

Résumé

In the rectangular region, we study nonlocal boundary value problems for the one-dimensional unsteady convection-diffusion equation of fractional order with variable coefficients, describing the diffusion transfer of a substance, as well as the transfer due to the motion of the medium. A priori estimates of solutions of nonlocal boundary value problems in differential form are derived by the method of energy inequalities. Difference schemes are constructed and analogs of a priori estimates in the difference form are proved for them, error estimates are given under the assumption of sufficient smoothness of solutions of equations. From the obtained a priori estimates, the uniqueness and stability of the solution from the initial data and the right part, as well as the convergence of the solution of the difference problem to the solution of the corresponding differential problem at the rate of $O(h^2+\tau^2)$.

Détail

Keywords: nonlocal boundary value problems, a priori estimate, nonstationary convection-diffusion equation, fractional order differential equation, fractional Caputo derivative.

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